To a certain extent sure, but there's a full spectrum. Football does have safer rules than it did a couple decades ago, so obviously there is and has been room for change. Rugby has similar sized guys (not quite as big, but big) and don't even wear protective gear (not that rugby players are immune to concussions). There's a big spectrum of rules in similar games, and football is still pretty far on the dangerous end of that spectrum.
One of the issues with football is that because they're wearing helmets they think that contact on the head is safe. It's incredibly not.
Rugby Union does a lot to regulate how contact happens. Rugby League (actually a different sport) has a combination of the lack of protection of Union and the outright violence of American Football. I don't follow League enough to know whether the lack of protection tends to lessen injuries. I understand it to be a game with a short shelf life for top players.
One of the issues with football is that because they're wearing helmets they think that contact on the head is safe. It's incredibly not.